Answer:
isn't an equivalence relation. It is reflexive but neither symmetric nor transitive.
Step-by-step explanation:
Let
denote a set of elements.
would denote the set of all ordered pairs of elements of
.
For example, with
,
and
are both members of
. However,
because the pairs are ordered.
A relation
on
is a subset of
. For any two elements
,
if and only if the ordered pair
is in
.
A relation
on set
is an equivalence relation if it satisfies the following:
- Reflexivity: for any
, the relation
needs to ensure that
(that is:
.)
- Symmetry: for any
,
if and only if
. In other words, either both
and
are in
, or neither is in
.
- Transitivity: for any
, if
and
, then
. In other words, if
and
are both in
, then
also needs to be in
.
The relation
(on
) in this question is indeed reflexive.
,
, and
(one pair for each element of
) are all elements of
.
isn't symmetric.
but
(the pairs in
are all ordered.) In other words,
isn't equivalent to
under
even though
.
Neither is
transitive.
and
. However,
. In other words, under relation
,
and
does not imply
.
Answer:
The area of APC is 70m². The area of triangle PMC is 35m².
Step-by-step explanation:
Let the area of triangle ABC be x.
It is given that AM is median, it means AM divides the area of triangle in two equal parts.
.....(1)
The point P is the midpoint of AB, therefore the area of APC and BPC are equal.
......(2)
The point P is midpoint of AB therefore the line PM divide the area of triangle ABM in two equal parts. The area of triangle APM and BPM are equal.
.....(3)
The area of triangle APM is 35m².



Therefore the area of triangle ABC is 140m².
Using equation (2).



Therefore the area of triangle APC is 70m².
Using equation (3), we can say that the area of triangle BPM is 35m² and by using equation (2), we can say that the area of triangle BPC is 70m².



Therefore the area of triangle PMC is 35m².
<span>There are 300 people in the enclosed space.
</span>
<span>Initially, one person had heard the rumor.</span>
Answer:
yo mama
Step-by-step explanation:
Answer:
This shows that the mean increases by 2.95
Step-by-step explanation:
Assume the given data is 2, 5, 6, 8
Mean = 2 +5+6+8/4
Mean = 21/4
Mean = 5.25
If number 20 is added, the data becomes 2, 5, 6, 8, 20
New mean = 2 +5+6+8+20/4
New mean = 41/5
New mean = 8.2
Taking the difference in the mean:
Difference = 8.2 - 5.25
Difference = 2.95
This shows that the mean increases by 2.95
<em>NB: The data used was assumed since we are not given any data in question</em>
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